How do I solve for c?

10^x is the inverse of log(x), so 10^(log(c)) = c = 10^22026

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The logarithm of a number to a given base is the exponent to which the base must be raised in order to produce that number.
For example, the logarithm of 1000 to base 10 is 3, because 3 factors of 10 multiply to a thousand: 10 × 10 × 10 equals 1000.

Since the base of the logarithm in the question is not specified, it is presumed to be base 10.

log c = 22,026
c = 10^22,026
.....or
c = 1 x 10^22,026
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☺☺☺☺☺☺☺☺☺this could be written as 1 followed by 22,026 zeroes !!!

log(10) c = 22026
=> c = 10^22026

log c = 22026
log c = log 10^22026
c = 10^22026